Question

三角形ABC中点,A(0,3) B(3,3) C(2,0)若直线x=a将三角形ABC分成面积相等的两部分,求实数a的值

Answer 1

AB=3,

过点C作平行于Y的直线交AB于D,

则CD=3,AD=(3-1)=2,

S⊿ABC=1/2*AB*CD=9/2,

S⊿ADC=1/2*AD*CD=6/2=3,

设,直线X=a与⊿ACD的交点为EF,交AD于E,交AC于F,

而,S⊿AEF=1/2S⊿ABC=9/4,

∵CD‖EF,S⊿AEF∽S⊿ADC,

则有S⊿AEF/S⊿ADC=AE^2/AD^2,

AE^2=AD^2*S⊿AEF/S⊿ADC=4*3/4=3,

AE=√3,而,AE=a,

∴a=√3.